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question:Which satellite has a longer period, satellite 1 in a certain circular orbit around a planet or satellite 2 in a larger circular orbit around the same planet?
answer:According to Kepler's third law for circular orbits, the period of a satellite's orbit is proportional to the cube root of the radius of its orbit. This means that satellites with larger orbits will always have longer periods. Therefore, satellite 2, which is in a larger circular orbit, must also have a longer period than satellite 1.
question:How might inflation of the U.S. dollar impact a Chinese international salesperson's efforts to increase exports to the United States?
answer:A Chinese international salesperson might be concerned about U.S. dollar inflation because it could lead to a reduction in the United States' demand for Chinese products. When the U.S. dollar inflates, the purchasing power of the currency decreases, making imported goods, such as those from China, relatively more expensive for American consumers. This could result in a decrease in demand for these products, thereby affecting the salesperson's export efforts. Additionally, higher inflation in the U.S. may prompt the U.S. Federal Reserve to raise interest rates to combat inflation, which could lead to a stronger U.S. dollar, further reducing the competitiveness of Chinese exports.
question:You deposit 6,848 in your account today. You make another deposit of 6,982 one year from today. How much will there be in your account at the end of year 1 if the interest rate is 6.8 percent per annum?
answer:The future value of an investment is the value of that investment at a future date, taking into account the effects of interest. In this case, we have two deposits, one at time 0 and one at time 1. We can use the formula for future value to calculate the total value of the investment at the end of year 1. The future value of the first deposit is: {eq} Future Value = 6,848 * (1 + 0.068 )^ {1} = 7,313.66 {/eq} The future value of the second deposit is: {eq} Future Value = 6,982 * (1 + 0.068 )^ {0} = 6,982 {/eq} The total future value of the investment is: {eq} Future Value = 7,313.66 + 6,982 = 14,295.66 {/eq} Deposit at (t0) = 6,848 Deposit at (t1) = 6,982 r = 6.8% {eq}begin{align*} Future Value & = Present Value * (1 + r )^ {n} & = 6,848 * (1 + 0.068 )^ {1} + 6,982 * (1 + 0.068 )^ {0} & = 7,313.66 + 6,982 & =14,295.66 end{align*} {/eq}
question:Divide the polynomial x^3-7 x^2-7 x+7 by -5. Express the quotient in simplified form.
answer:The quotient, when x^3-7 x^2-7 x+7 is divided by -5, is expressed as: -frac{1}{5}x^3 + frac{7}{5}x^2 + frac{7}{5}x - frac{7}{5}